Before We Start Cooking...

Before we start cooking, lets start with some basics. If you want to cook great food on a small budget, there is some equipment you should own. 
First, you need some standard pots and pans. You will also need spatulas, wooden spoons,whisks, etc. to use with these pots and pans. No need for anything fancy. If you don't have any, I suggest Target, Walmart, or Ikea, which have fairly inexpensive kitchen supplies. Thrift stores are also an option, just be smart and don't buy something that will break the first time you use it. Family and friends are also a great resource. Just let them know you need some and chances are they'll give you the stuff they were thinking about getting rid of, that's how I got mine.

1.6 quart slow-cooker
$16.99 at Target

Second, you will need a 9x13 inch or 8x8 inch glass baking pan. Pyrex or Anchor brands are the best and will last forever unless you drop it. 
Third, I suggest you get a slow-cooker. Slow-cookers are great for making just about anything, such as soup, chicken, beans, even bread and cake. Also, using a slow-cooker requires very little effort. If you are just cooking for a few people, I suggest a 2 quart slow-cooker, which will cost you $20 or less at Target or Walmart.
Fourth, I strongly suggest that you get a rice cooker/food steamer, it will make your life so much easier. Rice is a very inexpensive food and is very good for you. If you follow the directions on the rice cooker, your rice will never burn, thus saving you money. A rice cooker that is also a food steamer is excellent because you can make an entire well-balanced meal by cooking rice on the bottom and steaming meat and vegetables on the top. If you are not cooking for a lot of people, I suggest a 4 to 6 cup rice cooker/food steamer, which will run you about $20 or less at Walmart or Target.

6 cup rice cooker/food steamer
$16.99 at Target

Fifth, if you want to do any baking you will need a rolling pin, baking sheets, and a wooden cutting board. Again, these don't have to be super nice. Target and Walmart have good prices on this sort of thing.